An evolving entropy floor in the intracluster gas?

Nongravitational processes, such as feedback from galaxies and their active nuclei, are believed to have injected excess entropy into the intracluster gas, and therefore to have modified the density profiles in galaxy clusters during their formation. Here we study a simple model for this so-called preheating scenario, and ask (1) whether it can simultaneously explain both global X-ray scaling relations and number counts of galaxy clusters, and (2) whether the amount of entropy required evolves with redshift. We adopt a baseline entropy profile that fits recent hydrodynamic simulations, modify the hydrostatic equilibrium condition for the gas by including ≈20% nonthermal pressure support, and add an entropy floor K0 that is allowed to vary with redshift. We find that the observed luminosity-temperature (L − T) relations of low-redshift (⟨ z⟩ = 0.05) HIFLUGCS clusters and high-redshift (⟨ z⟩ = 0.80) WARPS clusters are best simultaneously reproduced with an entropy floor that evolves from ≈200 h^−1/3 keV cm^ 2 at z ≈ 0.8 to ≳300 h^−1/3 keV cm^ 2 at z < 0.05. This evolution may take place predominantly at low redshift (z≲ 0.2). If we restrict our analysis to the subset of bright (kT≳ 3 keV) clusters, we find that the evolving entropy floor can mimic a self-similar evolution in the L − T scaling relation. This degeneracy with self-similar evolution is, however, lifted when 0.5 keV ≲ kT≲ 3 keV clusters are included. Using the cosmological parameters from the WMAP 3 yr data, but treating σ8 as a free parameter, our model can reproduce the number counts of the X-ray galaxy clusters in the 158 deg2 ROSAT PSPC survey, with a best-fit value of σ8 = 0.80 ± 0.05.